Realization of quantum gates by Lyapunov control

We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schrödinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in...

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Bibliographic Details
Published in:Physics letters. A 2014-02, Vol.378 (9), p.699-704
Main Authors: Hou, S.C., Wang, L.C., Yi, X.X.
Format: Article
Language:English
Subjects:
CNOT gate
Control systems
Design engineering
Equivalence
Gates
Ising model
Local equivalence class
Lyapunov control
Operators
Quantum gate
Schroedinger equation
Solid state physics
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Summary:We propose a Lyapunov control design to achieve specific (or a family of) unitary time-evolution operators, i.e., quantum gates in the Schrödinger picture by tracking control. Two examples are presented. In the first, we illustrate how to realize the Hadamard gate in a single-qubit system, while in the second, the controlled-NOT (CNOT) gate is implemented in two-qubit systems with the Ising and Heisenberg interactions. Furthermore, we demonstrate that the control can drive the time-evolution operator into the local equivalence class of the CNOT gate and the operator keeps in this class forever with the existence of Ising coupling. •A Lyapunov control design is proposed to prepare quantum gates.•Any one-qubit gates can be implemented.•The CNOT gate is implemented with different Hamiltonians.•Local equivalence class of the CNOT gate is achieved.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2014.01.008